CHAPTER 7
1.
Assume that the oneperiod spot interest rate is 3 percent and the twoperiod spot interest
rate is 6 percent.
Answer the following questions:
(a) What is the present value of $100 received one year from now?
(b) What is the present value of $100 received two years from now?
(c) You are going to receive $100 two years from now.
What is its time 1 value?
What
is the forward interest rate?
(d) Suppose you invest $1 today at the twoperiod spot interest rate; what is its value at
time 2?
Alternatively you invest $1 at the oneperiod spot rate and reinvest at the
forward interest rate; what is the value at time 2?
How do these two investments
compare?
R
0,1
= 3%
R
0,2
= 6%
a.
$97.09
=
1.03
100
=
PV
b.
$89.00
=
)
(1.06
100
=
PV
2
c.
(1 + R
0,2
)
2
= (1 + R
0,1
)(1 + f
0,2
)
(1 + 0.06)
2
= (1.03)(1 + f
0,2
)
f
0,2
= 9.087%
Time 1 value =
01
.
1
9
$
=
1.0909
100
d.
1(1 + R
0,2
)
2
= 1(1+ 0.06)
2
= $1.12
1(1 + R
0,1
)(1 + f
0,2
) = 1(1.03)(1.0909) = $1.12
2.
Treasury strips with $100 par values have the following prices: oneperiod, $90; two
period, $80.
Answer the following questions:
(a) What are the oneperiod and twoperiod spot interest rates?
(b) What is the forward interest rate?
(c) If you invest $1 in oneperiod strips, what is the value after one period?
(d) If you invest $1 in twoperiod strips, what is the value after two periods?
(e) If you invest $1 at time 1 at the forward interest rate implied by the strips, what is the
value of this dollar at time 2?
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11.11%
=
R
R
+
1
100
=
90
0,1
0,1
11.80%
=
R
)
R
+
(1
100
=
80
0,2
2
0,2
b.
(1 + R
0,2
)
2
= (1 + R
0,1
)(1 + f
0,2
)
(1.1180)
2
= (1.1111)(1 + f
0,2
)
f
0,2
= 12.50%
c.
1(1.1111) = $1.11
d.
1(1.1180)
2
= $1.25
e.
1(1.1250) = $1.1250
3.
Treasury strips with $100 par values have the following prices: oneperiod, $94; two
period, $87.
You are going to receive an annuity of $100 for the next two periods.
What
is the present value of this annuity?
What is the time 1 value of this annuity?
What is the
time 2 value of this annuity?
PVA = (100)(0.94) + (100)(.87) = $181.00
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 Spring '08
 DUDLEY
 Interest Rates, Debt, Interest, Interest Rate, Forward contract, Forward price, Spot price

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